In [1]:
import geopandas as gpd
import matplotlib.pyplot as plt
import pandas as pd
import numpy as np

pd.set_option('display.max_columns', 500)

Lab 4: Fire Service Coverage Analysis - Maximal Covering Location Problem¶

For this lab we return to Fire Service Coverage seeking to assess tradeoffs in service against costs of maintaining different levels of stations.
Instead of covering all demand, the modeling approach tries to maximize the demand covered.
Specifically, we will employ the maximal covering location problem.
Instead of minimizing the number of facilities needed in a previous lab, we now introduce a parameter, $p$, representing a fixed number of facilities to keep in the system.

In Lab 4, there are three research questions we want to look into.

  1. Does a change in demand representation impact the optimization results?
  2. How can a service system be evaluated to prioritize demand maximization?
  3. Can the analysis process be generalized in order to replicate the approach using different demand representations?

The coverage standard for this lab will be fixed at 8000m.

In [2]:
S = 8000

Step 1. Prepare your dataset¶

Task: Load the three datasets and convert blocks and stations crs into the same one as FDs.crs.¶

  • It is because FDs is in a crs using meter as linear unit.
In [3]:
# Note: it might take time, as FD is a huge file.

FDs = gpd.read_file("Data/California_Fire_Districts.shp")   # load a shapefile containing California Fire District here
blocks = gpd.read_file("Data/sbBlocks_pop.shp")  # Load a shapefile containing Santa Barbara County blocks here
stations = gpd.read_file("Data/Fire_Stations_SBC.shp")  # Load a shapefile containing Fire Stations in Santa Barbara County here
In [4]:
FDs
Out[4]:
OBJECTID County FDID MACSID Name Address City Zip FireChief Phone Notes LastUpdate Website CALFIREUni SHAPE_Leng SHAPE_Area geometry
0 1 ALAMEDA 01005 ALA ALAMEDA FD 1300 PARK ST ALAMEDA 94501 NICHOLAS LUBY (510) 337‐2100 None 2018-06-21 https://www.alamedaca.gov/Departments/Fire-Dep... SCU 53100.838603 6.064225e+07 POLYGON ((-201596.954 -22267.837, -201603.038 ...
1 2 ALAMEDA 01008 ACF ALAMEDA COUNTY FD 6363 CLARK AVE DUBLIN 94568 WILLIAM L. MCDONALD (925) 833‐3473 None 2018-06-21 https://fire.acgov.org/index.page SCU 530457.107901 1.323031e+09 MULTIPOLYGON (((-175442.453 -53077.073, -17553...
2 3 ALAMEDA 01010 ALB CITY OF ALBANY FD 1000 SAN PABLO AVE ALBANY 94706 JAMES BOITO (510) 528‐5770 None 2018-06-21 https://www.albanyca.org/departments/fire-depa... SCU 20088.685628 1.370118e+07 POLYGON ((-201563.420 -10606.685, -201501.465 ...
3 4 ALAMEDA 01015 BER BERKELEY FD 2100 MLK JR WAY, 2ND FLOOR BERKELEY 94704 DAVID SPRAGUE (510) 981‐3473 None 2018-06-21 https://www.cityofberkeley.info/fire/ SCU 40101.143624 4.576781e+07 POLYGON ((-199372.313 -10022.195, -199339.870 ...
4 5 ALAMEDA 01040 FRE FREMONT FD 3300 CAPITOL AVE FREMONT 94538 CURTIS JACOBSON (510) 494‐4200 None 2018-06-21 https://www.fremont.gov/FireDepartment SCU 112154.310535 2.371594e+08 POLYGON ((-174294.970 -43700.784, -171936.393 ...
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
740 1051 SAN DIEGO 37224 SYC SYCUAN FD 5449 SYCUAN RD EL CAJON 92019 ZACHARY CARILLO (619) 445‐2893 None 2023-03-09 http://www.sycuanfire.com/ SDU 37785.328123 8.982372e+06 MULTIPOLYGON (((297409.208 -575061.437, 297410...
741 1052 SAN DIEGO None  UNSERVED None None None None None None 2023-03-09 None SDU 45330.418511 7.563897e+06 MULTIPOLYGON (((282015.611 -595689.809, 282087...
742 1053 SAN DIEGO 37175 VCF VALLEY CENTER FPD 28234 LILAC ROAD VALLEY CENTER 92082 JOSEF NAPIER (760) 751‐7600 None 2023-03-09 https://www.valleycenterfire.com/ SDU 143517.569373 2.105188e+08 MULTIPOLYGON (((276424.489 -517951.013, 276425...
743 1054 SAN DIEGO 37235 VJS VIEJAS FD 19854 VIEJAS GRADE ROAD ALPINE 91901 BOB PFOHL (619) 445‐7772 None 2023-03-09 https://viejasbandofkumeyaay.org/modern-govern... SDU 15883.245366 6.842021e+06 POLYGON ((309343.124 -566700.191, 309344.725 -...
744 1055 SAN DIEGO 37170 VTA VISTA FD AND FPD 200 CIVIC CENTER DR VISTA 92084 NED VANDER POL (760) 726‐1340 None 2023-03-09 https://www.cityofvista.com/departments/fire-d... SDU 72732.586859 9.194203e+07 POLYGON ((262798.704 -523482.702, 262810.008 -...

745 rows × 17 columns

Task: Look into the following Fire District maps.¶

There are many Fire Districts in California.
We are only going to focus in the "Santa Barbara County Fire District".
In the second map, note that there are many other Fire Districts in Santa Barbara County.
Though it's not shown on the map, they have some overlapping area, which means the area is co-operated by multiple Fire Districts.

In [5]:
blocks = blocks.to_crs(FDs.crs)
In [6]:
FDs.plot("Name")
Out[6]:
<Axes: >
No description has been provided for this image
In [7]:
FDs = FDs.loc[FDs.intersects(blocks.unary_union)].reset_index(drop=True)
FDs.plot("Name", legend=True, figsize=(10,10))
Out[7]:
<Axes: >
No description has been provided for this image
In [8]:
FDs
Out[8]:
OBJECTID County FDID MACSID Name Address City Zip FireChief Phone Notes LastUpdate Website CALFIREUni SHAPE_Leng SHAPE_Area geometry
0 89 KERN 15010 KRN KERN CO FD 5642 VICTOR ST BAKERSFIELD 93308 AARON DUNCAN (661) 391‐7000 None 2018-06-21 https://kerncountyfire.org/ KRN 998841.649563 1.921083e+10 MULTIPOLYGON (((207559.325 -315382.144, 207622...
1 304 SAN LUIS OBISPO 40080 SLC SAN LUIS OBISPO CO FD 635 N SANTA ROSA ST SAN LUIS OBISPO 93405 JOHN OWENS (805) 543‐4244 None 2018-06-21 https://calfireslo.org/ SLU 940256.942591 8.344077e+09 MULTIPOLYGON (((-58528.672 -319737.906, -58473...
2 316 SANTA BARBARA 42005 CRP CARPINTERIA SUMMERLAND FPD 1140 EUGENE PLACE, SUITE A CARPINTERIA 93013 GREG FISH (805) 684‐4591 None 2018-06-21 https://www.carpfire.com/ SBC 49534.138992 1.010901e+08 POLYGON ((50973.663 -398386.099, 50969.942 -39...
3 317 SANTA BARBARA 42030 MTO MONTECITO FPD 595 SAN YSIDRO RD SANTA BARBARA 93108 KEVIN TAYLOR (805) 969‐7762 None 2018-06-21 https://www.montecitofire.com/ SBC 39911.074682 3.644463e+07 POLYGON ((35557.315 -399389.055, 35295.841 -39...
4 318 SANTA BARBARA 42035 SBC SANTA BARBARA CFD 4410 CATHEDRAL OAKS RD SANTA BARBARA 93110 MARK A. HARTWIG (805) 681‐5500 None 2018-06-21 https://www.sbcfire.com/ SBC 778360.396807 3.666998e+09 MULTIPOLYGON (((23728.804 -401033.857, 23715.3...
5 396 VENTURA 56020 VNC VENTURA COUNTY FPD 165 DURLEY AVE CAMARILLO 93010 DUSTIN GARDNER (805) 389‐9710 None 2018-06-21 https://vcfd.org/ VNC 840086.616548 4.239353e+09 MULTIPOLYGON (((72888.961 -429800.719, 72849.7...
6 647 SANTA BARBARA 42010 GUA GUADALUPE FD 918 OBISPO ST GUADALUPE 93434 MICHAEL CASH (805) 356‐3905 None 2022-02-10 https://ci.guadalupe.ca.us/fire/ SBC 14598.470583 3.446183e+06 POLYGON ((-52159.523 -337901.424, -52142.953 -...
7 662 SANTA BARBARA 42040 SMR SANTA MARIA FD 314 WEST COOK ST #8 SANTA MARIA 93458 TODD TUGGLE (805) 925‐0951 None 2022-02-14 https://www.cityofsantamaria.org/city-governme... SBC 71542.884890 6.075262e+07 MULTIPOLYGON (((-36710.959 -344913.125, -36707...
8 676 SANTA BARBARA 42025 STB SANTA BARBARA CITY FD 925 CHAPALA ST SANTA BARBARA 93101 CHRIS MAILES (805) 965‐5254 None 2022-02-14 https://www.santabarbaraca.gov/gov/depts/fire/... SBC 81431.348424 5.056587e+07 MULTIPOLYGON (((15469.272 -397501.519, 15472.5...
9 678 SANTA BARBARA 42015 LMP LOMPOC FD 115 SOUTH G ST LOMPOC 93436 BRIAN FALLON (805) 736‐4513 None 2022-02-14 https://www.cityoflompoc.com/government/depart... SBC 38950.291184 3.025921e+07 MULTIPOLYGON (((-42597.382 -377627.460, -42626...

Question 1: Sort out a Fire District out of FDs GeoDataFrame. The district must have its 'Name" column value, "SANTA BARBARA CFD". ( 1 pt )¶

In [9]:
SBC_FD = FDs[FDs['Name'] == "SANTA BARBARA CFD"].reset_index(drop=True)
In [10]:
SBC_FD
Out[10]:
OBJECTID County FDID MACSID Name Address City Zip FireChief Phone Notes LastUpdate Website CALFIREUni SHAPE_Leng SHAPE_Area geometry
0 318 SANTA BARBARA 42035 SBC SANTA BARBARA CFD 4410 CATHEDRAL OAKS RD SANTA BARBARA 93110 MARK A. HARTWIG (805) 681‐5500 None 2018-06-21 https://www.sbcfire.com/ SBC 778360.396807 3.666998e+09 MULTIPOLYGON (((23728.804 -401033.857, 23715.3...

Task: Run following cell, "del FDs". Note: It will delete FDs variable.¶

We do this because FDs contains a large shapefile, which might burden your RAM.

In [11]:
del FDs

Task: take a subset of stations, within SBC_FD.¶

NOTE: don't forget to RESET_INDEX() whenever you take a subset!

In [12]:
stations = stations.to_crs(blocks.crs)
In [13]:
stations = stations.loc[stations.within(SBC_FD.unary_union)].reset_index(drop=True)
In [14]:
len(stations)
Out[14]:
28

Question 2: Plot the blocks GeoDataFrame. ( 2 pts )¶

  • Firstly, update the blocks GeoDataFrame's geometry column to have block centroids, not block polygons ( 0.5 pt )
  • Secondly, take a subset of blocks which is within the SBC_FD area ( 0.5 pt )
  • Thirdly, plot blocks GeoDataFrame with "Population" column. ( 1 pt )
    • figsize=(10,10)
    • opacity must be 0.4
    • take a cmap (colormap) that you like from this webpage (https://matplotlib.org/stable/users/explain/colors/colormaps.html).
    • markersize must be proportional to the column, "Population"
    • ensure you have legend
    • Plot with stations GeoDataFrame

Hint: when there's something you don't know about plot function, refer to this document page (https://geopandas.org/en/stable/docs/reference/api/geopandas.GeoDataFrame.plot.html)! Also, you can Google or ask chatGPT :)

In [15]:
blocks['geometry'] = blocks['geometry'].centroid
In [16]:
blocks = blocks.loc[blocks.within(SBC_FD.unary_union)].reset_index(drop=True)
In [17]:
fig, ax = plt.subplots(figsize=(10, 10))
SBC_FD.plot(ax=ax, color='none', edgecolor='blue', zorder=10)
blocks.plot(
    ax=ax,
    column='Population',
    cmap='viridis',
    legend=True,
    markersize=blocks['Population']*0.1,
    alpha=0.4,
    legend_kwds={'label':"Population"}
)
stations.plot(ax=ax, color='red', markersize=50, label='Stations', zorder=5)

plt.title("population of blocks")
plt.show
Out[17]:
<function matplotlib.pyplot.show(close=None, block=None)>
No description has been provided for this image
In [18]:
len(blocks)
Out[18]:
3224

Step 2. Conduct MCLP¶

Decision Variables: \begin{align*} & x_j = \begin{cases} 1, & \text{if facility $j$ is open}, \\ 0, & \text{otherwise}. \end{cases} \\ & y_i = \begin{cases} 1, & \text{if demand $i$ is covered}, \\ 0, & \text{otherwise}. \end{cases} \end{align*}

Parameters: \begin{align*} & I = \text{number of demands}, \\ & J = \text{number of facilities}, \\ & S = \text{Coverage Distance Standard}, \\ & a_i = \text{Weight assigned to demand $i$}, \\ & D_{ij} = \text{Distance between demand $i$ and facility $j$}, \\ & N_i = \{ j \in J \, | \, D_{ij} \leq S \}, \\ & P = \text{the number of facilities to be opened}. \end{align*}

Objective Function: \begin{align*} \text{Maximize:} \quad & \sum_{i=1}^{I} a_i y_i \end{align*}

Constraints: \begin{align*} \text{Subject to:} \quad & \sum_{j \in N_i} x_j \geq y_i, \quad \forall i \in I \\ & \sum_{j=1}^{J} x_j \leq P, \\ & x_j, y_i \in \{0, 1\}, \quad \forall i, j. \end{align*}

Task: Based on the mathematical Model, set the I and J values correctly.¶

  • In this section, we will consider each block as demand $i$
  • we will consider each existing fire station as facility $j$
  • In the beginning of this lab, we defined our S value to be 8000 meter, 8 km.
  • Pick any P that is less than current number of stations :)
In [19]:
I = len(blocks)
J = len(stations)
P = 20

Task: We are going to have block's population as weight assigned to demand. Define $a_i$.¶

In [20]:
a_i = blocks['Population']

Task: Create $D_{ij}$ variable using Euclidean Distance between demand $i$ and facility $j$.¶

In [21]:
D_ij =[[np.sqrt((blocks['geometry'].x[i] - stations.geometry.x[j])**2 + (blocks['geometry'].y[i] - stations.geometry.y[j])**2)
                 for j in range(J)] for i in range(I)]

Question 3: Create $N_i$ variable in list format. ( 1 pt )¶

  • Previously, $N_i$ in dictionary is introduced.
  • With your understanding so far, list format of $N_i$ can also be created.
  • You can use double for-loops, or list comprehension.
In [22]:
# This is a hint for students who want to do it with list comprehension


# Creating a two-dimensional list
matrix = [[1, 2, 3],
          [4, 5, 6],
          [7, 8, 9],
          [10, 11, 12]]

# Using list comprehension to filter even numbers from the matrix
# The '%' symbol in Python is called the modulo operator. 
    #It returns the remainder of the division of the left operand by the right operand.
even_numbers = [[matrix[r][c] for c in range(len(matrix[0])) if matrix[r][c]%2 == 0]
                for r in range(len(matrix))]

print(even_numbers)
[[2], [4, 6], [8], [10, 12]]
In [23]:
N_i = [[j for j in range(J) if D_ij[i][j] <= S] for i in range(I)]
In [24]:
N_i
Out[24]:
[[18],
 [],
 [],
 [15, 16],
 [],
 [],
 [0, 1, 18],
 [],
 [5, 6, 7, 26],
 [0, 1, 18],
 [0, 1, 18],
 [15, 16],
 [0, 1, 18, 27],
 [0, 1, 18, 27],
 [0, 1, 18],
 [0, 1, 18],
 [0, 1, 18, 27],
 [0, 1, 18],
 [0, 1, 18],
 [0, 1, 17, 18, 27],
 [0, 1, 18],
 [0, 1, 18],
 [0, 1, 18],
 [0, 1, 17, 18, 27],
 [0, 1, 18],
 [0, 1, 18],
 [0, 1, 17, 18, 27],
 [0, 1, 17, 18, 27],
 [0, 1, 18, 27],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [13, 15],
 [13, 15],
 [13, 15],
 [13],
 [13],
 [13],
 [13, 15],
 [13],
 [13],
 [13],
 [],
 [],
 [],
 [],
 [],
 [],
 [4, 5, 26],
 [],
 [],
 [],
 [],
 [],
 [],
 [],
 [],
 [],
 [],
 [],
 [23],
 [23],
 [23],
 [23],
 [23],
 [23],
 [],
 [23],
 [],
 [],
 [],
 [25],
 [],
 [],
 [],
 [],
 [],
 [8, 9, 10, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 10, 19, 21, 24],
 [8, 9, 10, 19, 24],
 [1, 17, 27],
 [1, 17, 27],
 [4, 5, 6, 7, 26],
 [4, 5, 6, 7, 26],
 [20, 21, 22, 24],
 [19, 20, 21, 22, 24],
 [15, 16],
 [8, 9, 10, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 10, 19, 20, 21, 22, 24],
 [8, 9, 10, 19, 20, 21, 24],
 [8, 9, 10, 19, 20, 21, 24],
 [8, 9, 10, 19, 21, 24],
 [8, 9, 10, 19, 24],
 [8, 9, 10, 19, 20, 21, 22, 24],
 [8, 9, 10, 19, 20, 21, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 10, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [],
 [],
 [4],
 [0, 1],
 [0, 1, 18],
 [0, 1],
 [0, 1],
 [0, 1],
 [0, 1, 3],
 [11],
 [2],
 [11],
 [13, 15, 16],
 [17, 27],
 [23],
 [19, 20, 21, 22, 24],
 [19, 20, 21, 22, 24],
 [13],
 [4, 5],
 [4, 5],
 [4, 5],
 [19, 20, 21, 22, 24],
 [8, 9, 10, 19, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [19, 20, 21, 22, 24],
 [8, 9, 10],
 [8, 9, 10],
 [8, 9, 10],
 [8, 9, 10],
 [8, 9, 10],
 [8, 9, 10],
 [0, 1, 18],
 [0, 1, 18],
 [15, 16],
 [9, 19, 20, 21, 22, 24],
 [9, 19, 20, 21, 22, 24],
 [9, 19, 20, 21, 22, 24],
 [9, 19, 20, 21, 22, 24],
 [9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [15, 16],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [],
 [15, 16],
 [1, 17, 27],
 [19, 20, 21, 22, 24],
 [15, 16],
 [19, 20, 21, 22, 24],
 [18],
 [16],
 [16, 18],
 [18],
 [18],
 [18],
 [18],
 [18],
 [18],
 [18],
 [15, 16],
 [18],
 [4, 5],
 [0, 1, 18],
 [18],
 [1, 18],
 [18],
 [0, 18],
 [0, 1, 18],
 [18],
 [18],
 [4, 5],
 [0, 1, 18],
 [0, 1, 18],
 [4, 5, 6, 7, 26],
 [4],
 [4, 5, 26],
 [4, 5],
 [4, 5, 6, 7, 26],
 [4, 5],
 [4, 5, 26],
 [4],
 [4, 5],
 [4, 5, 6, 7, 26],
 [4, 5, 6, 7, 26],
 [4, 5],
 [4, 5],
 [4, 5, 6, 7, 26],
 [15, 16],
 [15, 16],
 [20, 21, 22, 24],
 [25],
 [25],
 [25],
 [25],
 [25],
 [],
 [0, 1, 18],
 [0, 1, 18],
 [],
 [0, 1, 18],
 [0, 1, 18],
 [26],
 [0, 1, 18],
 [0, 1, 18],
 [0, 1, 18],
 [0, 1, 18],
 [20, 21, 22],
 [0, 1, 18],
 [20, 21, 22, 24],
 [0, 1, 18],
 [0, 1, 18],
 [0, 1, 18],
 [20, 21, 22, 24],
 [0, 1, 18],
 [0, 1, 18],
 [0, 1, 18],
 [0, 1, 18],
 [0, 1, 18],
 [0, 1, 17, 27],
 [0, 1, 18],
 [0, 1, 17, 27],
 [0, 1, 17, 27],
 [0, 1, 17, 27],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [0, 1, 17, 27],
 [0, 1, 17, 27],
 [0, 1, 17, 27],
 [0, 1, 18],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [0, 1, 18],
 [0, 1, 17, 27],
 [0, 1, 17, 27],
 [0, 1, 18],
 [18],
 [],
 [],
 [11],
 [],
 [],
 [],
 [11],
 [23],
 [5],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [0, 1, 18],
 [0, 1, 18],
 [0, 1, 18],
 [0, 1, 18],
 [0, 1, 18],
 [0, 1, 18],
 [17, 27],
 [17, 27],
 [4, 5],
 [4, 5],
 [0, 1, 18],
 [0, 1, 18],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [15, 16],
 [14],
 [4, 5, 6, 7, 26],
 [15, 16],
 [9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [15, 16],
 [1, 2, 3],
 [15, 16],
 [4, 5],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 10, 19, 20, 21, 24],
 [15, 16],
 [0, 1, 17, 27],
 [15, 16],
 [],
 [8, 9, 10, 19, 24],
 [],
 [0, 1, 18],
 [15, 16],
 [15, 16],
 [5, 6, 7, 26],
 [],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [9, 19, 20, 21, 22, 24],
 [9, 19, 20, 21, 22, 24],
 [9, 19, 20, 21, 22, 24],
 [9, 19, 20, 21, 22, 24],
 [9, 19, 20, 21, 22, 24],
 [9, 19, 20, 21, 22, 24],
 [9, 19, 20, 21, 22, 24],
 [9, 19, 20, 21, 22, 24],
 [9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 10, 19, 20, 21, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [15, 16],
 [4, 5, 6, 7, 26],
 [4, 5, 6, 7, 26],
 [4, 5, 6, 7, 26],
 [8, 9, 19, 20, 21, 22, 24],
 [19, 20, 21, 22, 24],
 [19, 20, 21, 22, 24],
 [15, 16],
 [15, 16],
 [15, 16],
 [19, 20, 21, 22, 24],
 [15, 16],
 [19, 20, 21, 22, 24],
 [15, 16],
 [15, 16],
 [15, 16],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 10, 19, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 10, 19, 21, 24],
 [8, 9, 10, 19, 21, 24],
 [8, 9, 10],
 [19, 20, 21, 22, 24],
 [19, 20, 21, 22, 24],
 [25],
 [25],
 [25],
 [25],
 [25],
 [25],
 [25],
 [5, 23],
 [5],
 [5, 23],
 [23],
 [23],
 [23],
 [23],
 [23],
 [4, 5, 6, 7, 26],
 [4, 5],
 [],
 [8, 9, 10],
 [],
 [],
 [],
 [8, 9, 10],
 [],
 [19, 20, 21, 22, 24],
 [17, 27],
 [],
 [15, 16],
 [19, 20, 21, 22, 24],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [0, 1, 18],
 [15, 16],
 [0, 1, 18, 27],
 [0, 1, 18, 27],
 [0, 1, 18, 27],
 [0, 1, 18],
 [0, 1, 18, 27],
 [0, 1, 18],
 [0, 1, 18],
 [0, 1, 18],
 [8, 9, 10, 19],
 [0, 1, 18, 27],
 [0, 1, 18, 27],
 [0, 1, 18],
 [],
 [4, 5],
 [19, 20, 21, 22, 24],
 [15, 16],
 [0, 1, 18],
 [17, 27],
 [17, 27],
 [4, 5],
 [15, 16],
 [4, 5, 6, 7, 26],
 [4, 5, 6, 7, 26],
 [4, 5, 6, 7, 26],
 [0, 1, 17, 27],
 [0, 1, 17, 27],
 [17, 27],
 [17, 27],
 [5, 6, 7, 26],
 [15, 16],
 [1, 17, 27],
 [1, 17, 27],
 [15, 16],
 [15, 16],
 [1, 17, 27],
 [0, 1, 18],
 [8, 9, 10, 19, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [6, 7],
 [6, 7, 26],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [6, 7, 25],
 [15, 16],
 [25],
 [4, 5],
 [],
 [],
 [25],
 [19, 20, 21, 22, 24],
 [19, 20, 21, 22, 24],
 [1, 17, 27],
 [1, 17, 27],
 [1, 17, 27],
 [1, 17, 27],
 [19, 20, 21, 22, 24],
 [9, 19, 20, 21, 22, 24],
 [0, 1, 18],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [13, 15, 16],
 [1, 17, 27],
 [0, 1, 17, 27],
 [18],
 [17, 27],
 [15, 16],
 [15, 16],
 [26],
 [1, 17, 27],
 [15, 16],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 10, 19, 20, 21, 22, 24],
 [0, 1, 3],
 [8, 9, 10, 19, 20, 21, 22, 24],
 [8, 9, 10, 19, 20, 21, 22, 24],
 [14],
 [17, 27],
 [17, 27],
 [17, 27],
 [17, 27],
 [5, 6, 7, 26],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [8, 9, 19, 20, 21, 22, 24],
 [5],
 [9, 19, 20, 21, 22, 24],
 [9, 19, 20, 21, 22, 24],
 [4, 5, 6, 7, 26],
 [4, 5, 6, 7, 26],
 [13, 15, 16],
 [19, 20, 21, 22, 24],
 [8, 9, 10, 19, 21, 24],
 [19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 10, 19, 20, 21, 22, 24],
 [8, 9, 10, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 10, 19, 20, 21, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 10, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 10, 19, 20, 21, 24],
 [8, 9, 10, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 10, 19, 20, 21, 22, 24],
 [8, 9, 10, 19, 20, 21, 22, 24],
 [8, 9, 10, 19, 20, 21, 22, 24],
 [8, 9, 10],
 [4, 5, 6, 7, 26],
 [8, 9, 19, 20, 21, 22, 24],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [17, 27],
 [4, 5, 6, 7, 26],
 [4, 5, 6, 7, 26],
 [5, 6, 7, 26],
 [15, 16],
 [15, 16],
 [0, 1, 18],
 [15, 16],
 [15, 16],
 [9, 19, 20, 21, 22, 24],
 [19, 20, 21, 22, 24],
 [9, 19, 20, 21, 22, 24],
 [19, 20, 21, 22, 24],
 [9, 19, 20, 21, 22, 24],
 [4, 5],
 [4, 5],
 [4, 5],
 [4, 5],
 [14],
 [],
 [],
 [],
 [14],
 [],
 [],
 [14],
 [],
 [],
 [14],
 [],
 [],
 [],
 [],
 [],
 [26],
 [],
 [2, 3],
 [13, 15, 16],
 [6, 7, 26],
 [2, 3],
 [0, 1, 18],
 [0, 1, 18],
 [0, 1, 18],
 [0, 1, 18],
 [15, 16],
 [],
 [],
 [],
 [],
 [],
 [],
 [],
 [],
 [],
 [],
 [],
 [],
 [],
 [11],
 [],
 [],
 [4, 5, 6, 7, 26],
 [4, 5, 6, 7, 26],
 [4, 5, 6, 7, 26],
 [4, 5, 6, 7, 26],
 [4, 5, 6, 7, 26],
 [4, 5, 6, 7, 26],
 [4, 5, 6, 7, 26],
 [4, 5, 6, 7, 26],
 [4, 5, 6, 7, 26],
 [4, 5],
 [4, 5, 6, 7, 26],
 [4, 5, 6, 7, 26],
 [4, 5, 6, 7, 26],
 [4, 5, 6, 7, 26],
 [4, 5, 6, 7, 26],
 [4, 5, 6, 7, 26],
 [4, 5, 6, 7, 26],
 [4, 5, 6, 7, 26],
 [5, 6, 7, 26],
 [4, 5, 6, 7, 26],
 [8, 9, 19, 20, 21, 22, 24],
 [9, 19, 20, 21, 22, 24],
 [8, 9, 10, 19, 20, 21, 24],
 [15, 16],
 [16],
 [],
 [19, 20, 21, 22, 24],
 [15, 16],
 [9, 19, 20, 21, 22, 24],
 [9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [0, 18],
 [19, 20, 21, 22, 24],
 [26],
 [14],
 [14],
 [18],
 [15, 16],
 [15, 16],
 [8, 9, 19, 20, 21, 22, 24],
 [15, 16],
 [],
 [8, 9, 10, 19, 20, 21, 24],
 [],
 [8, 9, 19, 20, 21, 22, 24],
 [14],
 [1, 17, 27],
 [9, 19, 20, 21, 22, 24],
 [4],
 [1, 17, 27],
 [8, 9, 10, 19, 20, 21, 22, 24],
 [23],
 [15, 16],
 [15, 16],
 [],
 [8, 9, 10, 19],
 [15, 16],
 [15, 16],
 [15, 16],
 [19, 20, 21, 22, 24],
 [15, 16],
 [],
 [],
 [],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [15, 16],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [19, 20, 21, 22, 24],
 [5, 6, 7, 26],
 [20, 21, 22, 24],
 [20, 21, 22, 24],
 [19, 20, 21, 22, 24],
 [19, 20, 21, 22, 24],
 [19, 20, 21, 22, 24],
 [19, 20, 21, 22, 24],
 [19, 20, 21, 22, 24],
 [19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [17, 27],
 [20, 21, 22, 24],
 [20, 21, 22, 24],
 [20, 21, 22, 24],
 [20, 21, 22, 24],
 [5, 6, 7, 26],
 [0, 1, 18],
 [0, 1, 18],
 [0, 1, 18],
 [0, 1, 18],
 [0, 1, 18],
 [8, 9, 19, 20, 21, 22, 24],
 [0, 1, 18],
 [0, 1, 18],
 [0, 1, 18],
 [0, 1, 18],
 [0, 1, 18],
 [0, 1, 18],
 [15, 16],
 [0, 1, 17, 27],
 [0, 1, 18],
 [0, 1, 18],
 [],
 [0, 1, 18],
 [15, 16],
 [0, 1, 18],
 [18],
 [18],
 [17, 27],
 [4],
 [4, 5],
 [],
 [],
 [],
 [25],
 [25],
 [25],
 [8, 9, 19, 20, 21, 22, 24],
 [25],
 [25],
 [25],
 [25],
 [25],
 [25],
 [25],
 [15],
 [25],
 [20, 21, 22, 24],
 [8, 9, 10, 19, 20, 21, 22, 24],
 [],
 [0, 1],
 [0, 1],
 [0, 1],
 [0, 1, 3],
 [19, 20, 21, 22, 24],
 [0, 1],
 [0, 1],
 [0, 1, 3],
 [0, 1, 3],
 [11],
 [11],
 [11],
 [11],
 [11],
 [11],
 [11],
 [4, 5],
 [5, 26],
 [4, 5, 26],
 [5],
 [4, 5, 23],
 [23],
 [5],
 [4, 5, 6, 7, 26],
 [5, 23],
 [4, 5],
 [4, 5],
 [4, 5],
 [5, 26],
 [5, 6, 7, 26],
 [6, 7, 25, 26],
 [5, 6, 7, 26],
 [6, 7, 26],
 [6, 7, 25, 26],
 [5, 6, 7, 26],
 [5, 6, 7, 26],
 [5, 6, 7, 26],
 [5, 6, 7, 26],
 [5, 6, 7, 26],
 [5, 6, 7, 26],
 [5, 6, 7, 26],
 [5, 6, 7, 26],
 [5, 6, 7, 26],
 [5, 6, 7, 26],
 [5, 6, 7, 26],
 [5, 6, 7, 26],
 [5, 6, 7, 26],
 [5, 6, 7, 26],
 [5, 6, 7, 26],
 [5, 6, 7, 26],
 [5, 6, 7, 26],
 [5, 6, 7, 26],
 [5, 6, 7, 26],
 [5, 6, 7, 26],
 [5, 6, 7, 26],
 [14],
 [4, 5, 6, 7, 26],
 [5, 6, 7, 26],
 [5, 6, 7, 26],
 [5, 6, 7, 26],
 [5, 6, 7, 26],
 [5, 6, 7, 26],
 [6, 7, 26],
 [5, 6, 7, 26],
 [6, 7, 26],
 [5, 6, 7, 26],
 [5, 6, 7, 26],
 [4, 5, 6, 7, 26],
 [5, 6, 7, 26],
 [5, 6, 7, 26],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [4, 5, 6, 7, 26],
 [4, 5, 6, 7, 26],
 [8, 9, 10, 19],
 [8, 9, 10, 19],
 [8, 9, 10, 19, 24],
 [20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [4, 5, 6, 7, 26],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 10, 19],
 [9, 19, 20, 21, 22, 24],
 [5, 6, 7, 26],
 [4, 5],
 [17, 27],
 [19, 20, 21, 22, 24],
 [4, 5],
 [8, 9, 10],
 [8, 9, 10, 19, 20, 21, 24],
 [8, 9, 10, 19],
 [8, 9, 10, 19, 24],
 [],
 [19, 20, 21, 22, 24],
 [],
 [13],
 [8, 9, 19, 20, 21, 22, 24],
 [9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 10, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [4, 5, 6, 7, 26],
 [],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 10, 19, 20, 21, 22, 24],
 [8, 9, 10, 19],
 [19, 20, 21, 22, 24],
 [15, 16],
 [15, 16],
 [16],
 [8, 9, 10, 19],
 [19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [15, 16],
 [15, 16],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 10, 19, 24],
 [],
 [17, 27],
 [15, 16],
 [15, 16],
 [15, 16],
 [15, 16],
 [0, 1, 17, 27],
 [8, 9, 10, 19, 24],
 [8, 9, 10, 19, 24],
 [8, 9, 10, 19, 24],
 [15, 16],
 [18],
 [14],
 [8, 9, 19, 20, 21, 22, 24],
 [],
 [15, 16],
 [],
 [15, 16],
 [],
 [],
 [14],
 [17, 27],
 [14],
 [14],
 [15, 16],
 [15, 16],
 [15, 16],
 [13, 15, 16],
 [8, 9, 10, 19, 20, 21, 24],
 [8, 9, 10, 19, 21, 24],
 [8, 9, 10, 19, 20, 21, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 10, 19, 20, 21, 24],
 [],
 [8, 9, 10, 19, 20, 21, 24],
 [],
 [8, 9, 19, 20, 21, 22, 24],
 [4, 5, 6, 7, 26],
 [8, 9, 10, 19, 20, 21, 24],
 [8, 9, 10, 19],
 [8, 9, 10, 19, 20, 21, 24],
 [8, 9, 10, 19, 21, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 19, 20, 21, 22, 24],
 [8, 9, 10, 19, 20, 21, 22, 24],
 ...]

Question 4: Complete the Optimization Model ( 6 pts )¶

In [25]:
import gurobipy as gp
from gurobipy import GRB

# Create a new Gurobi model
mclp = gp.Model("Maximal_Covering_Location")

# Decision Variables
x = mclp.addVars(J, vtype=GRB.BINARY, name="x")       # Facility is open or not
y = mclp.addVars(I, vtype=GRB.BINARY, name="y")       # Demand is covered or not

# Objective Function
mclp.setObjective(gp.quicksum(a_i[i]*y[i] for i in range(I)), GRB.MAXIMIZE)

# Constraints
# Each demand must be covered by neighboring facility
mclp.addConstrs(gp.quicksum(x[j] for j in N_i[i]) >= y[i] for i in range (I))

# Number of opened facilities must not exceed P
mclp.addConstr(gp.quicksum(x[j] for j in range(J)) <= P)

# Optimize the model
mclp.optimize()
Set parameter Username
Academic license - for non-commercial use only - expires 2025-05-10
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0x06e3d55a
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3225 rows and 3252 columns
Presolve time: 0.01s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 1 (of 8 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%

Question 5: Take a subset of stations based on the model output. ( 1 pt )¶

In [27]:
open_stations_indices = [j for j in range(J) if x[j].x > 0.5]
open_stations= stations.iloc[open_stations_indices]
open_stations
Out[27]:
Label Desig Number Type Department Name_other Address Notes Num_2019 Scale Latitude Longitude geometry
1 VAFB-42 AFV-2 42 Fire Station Vandenberg Fire Department None New Mexico Ave., Vandenberg, CA None 42 0 34.7345 -120.534 POINT (-48865.923 -364526.814)
2 VAFB-44 AFV-4 44 Fire Station Vandenberg Fire Department None Arguello Rd., Vandenberg, CA None 44 0 34.6125 -120.570 POINT (-52227.109 -378048.804)
4 SBC-31 SBC-31 31 Fire Station Santa Barbara County Fire Department None 168 W Hwy 246, Buellton, CA 93427 None 31 900 34.6132 -120.197 POINT (-18043.064 -378107.359)
5 SBC-30 SBC-30 30 Fire Station Santa Barbara County Fire Department None 1644 Oak St., Solvang, CA 93464 None 30 900 34.5935 -120.142 POINT (-12980.623 -380307.178)
6 SBC-32 SBC-32 32 Fire Station Santa Barbara County Fire Department None 906 Airport Rd., Santa Ynez, CA 93460 None 32 1100 34.6075 -120.069 POINT (-6364.715 -378763.420)
9 SBC-13 SBC-13 13 Fire Station Santa Barbara County Fire Department None 4570 Hollister, Santa Barbara, CA 93110 None 13 1000 34.4386 -119.780 POINT (20241.872 -397479.331)
11 SBC-27 SBC-27 27 Fire Station Santa Barbara County Fire Department None 41 Newsome St., New Cuyama, CA 93254 None 27 700 34.9457 -119.682 POINT (29023.176 -341164.220)
12 LPF-35 LPF-35 35 Fire Station LPF Pine Canyon 8145 Hwy 166, Santa Maria, CA 93454 None 35 0 35.0294 -120.194 POINT (-17696.745 -331903.082)
13 SBC-23 SBC-23 23 Fire Station Santa Barbara County Fire Department None 5003 Depot Ave., Santa Maria, CA 93454 None 23 600 34.8666 -120.294 POINT (-26898.330 -349956.970)
14 SBC-24 SBC-24 24 Fire Station Santa Barbara County Fire Department None 99 Centennial, Los Alamos, CA 93440 None 24 800 34.7451 -120.280 POINT (-25603.519 -363453.395)
15 SBC-26 SBC-26 26 Fire Station Santa Barbara County Fire Department None 1600 Tiffany Park Court, Santa Maria, CA 93455 None 26 600 34.8657 -120.402 POINT (-36721.414 -350025.728)
16 SBC-21 SBC-21 21 Fire Station Santa Barbara County Fire Department None 335 Union Ave., Orcutt, CA 93455 None 21 600 34.8644 -120.444 POINT (-40540.132 -350149.951)
17 SBC-34 SBC-34 34 Fire Station Santa Barbara County Fire Department None 3510 Harris Grade Rd., Lompoc, CA 93436 None 34 1000 34.6909 -120.447 POINT (-40958.522 -369401.362)
18 VAFB-43 AFV-3 43 Fire Station Vandenberg Fire Department None El Rancho Rd., Vandenberg, CA None 43 0 34.7882 -120.565 POINT (-51640.364 -358544.456)
19 SBC-12 SBC-12 12 Fire Station Santa Barbara County Fire Department None 5330 Calle Real, Goleta, CA 93117 None 12 900 34.4429 -119.812 POINT (17256.190 -397008.608)
22 SBC-11 SBC-11 11 Fire Station Santa Barbara County Fire Department None 6901 Frey Way, Goleta, CA 93117 None 11 700 34.4258 -119.870 POINT (11934.816 -398917.392)
23 SBC-38 SBC-38 38 Fire Station Santa Barbara County Fire Department None 17200 Mariposa Reina, Gaviota, CA 93117 None 38 800 34.4767 -120.214 POINT (-19690.488 -393256.876)
25 SBC Camp 1 SBC-CR None Camp Santa Barbara County Fire Department Cachuma Camp Lakeview Dr., Lake Cachuma, CA Crew 10, Crew 11 CREW 1200 34.5688 -119.948 POINT (4737.414 -383052.783)
26 CHU-1 CHU-1 1 Fire Station Chumash Fire Department Chumash 3300 Hwy 246, Santa Ynez, CA 93460 None 1 0 34.6088 -120.089 POINT (-8141.257 -378616.310)

Question 6: Plot the open_stations and their coverage buffers with the demand buffers. ( 2 pts )¶

  • Copy and Paste the plotting code from Question 2.
  • Replace stations with open_stations.
  • Add another plot function which plots the buffer with buffer distance S from each open_station.
    • The coverage buffer shouldn't have facecolor
    • Buffer Boundary must be dashed lines. (ask chatGPT of google how to do this!)
In [28]:
open_stations['buffer'] = open_stations.geometry.buffer(S)
fig, ax = plt.subplots(figsize=(10, 10))
SBC_FD.plot(ax=ax, color='none', edgecolor='blue', zorder=10)
blocks.plot(
    ax=ax,
    column='Population',
    cmap='viridis',
    legend=True,
    markersize=blocks['Population']*0.1,
    alpha=0.4,
    legend_kwds={'label':"Population"}
)
open_stations.plot(ax=ax, color='red', markersize=50, label='Stations', zorder=5)

for buffer in open_stations['buffer']:
    gpd.GeoSeries(buffer).boundary.plot(ax=ax, linestyle='--', color='green')

plt.title("population of blocks")
plt.show
/opt/anaconda3/lib/python3.11/site-packages/geopandas/geodataframe.py:1525: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame.
Try using .loc[row_indexer,col_indexer] = value instead

See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
  super().__setitem__(key, value)
Out[28]:
<function matplotlib.pyplot.show(close=None, block=None)>
No description has been provided for this image

Step 3. Functionize / Modularize¶

Here, we will functionize our optimization model.
Sothat with given P value, the model can be solved.

Question 7: Functionize your code out of Question 4 and 5 ( 2 pts )¶

  • start defining a function named, "solve_mclp". ( 0.5 pts )
  • The function takes one argument, P. ( 0.5 pts )
  • Within the function, copy and paste the code you did for Question 4 and 5. ( 0.5 pts )
  • Then, add the last line of code, to return open_stations, and mclp.obj_val ( 0.5 pts )
In [29]:
# Let me give you functionize example.
# For more, refer to Lab 0.

sample_list = [1,2,3,4]

def sum_array(a):
    s = 0
    a = np.array(a)
    for num in a:
        s += num
    return s, a # Return the summation of all elements, and the original array

sum_array(sample_list)
Out[29]:
(10, array([1, 2, 3, 4]))
In [30]:
## PUT YOUR FUNCTION HERE!!!##
def solve_mclp(P):
    mclp = gp.Model("Maximal_Covering_Location")
    x = mclp.addVars(J, vtype=GRB.BINARY, name="x") 
    y = mclp.addVars(I, vtype=GRB.BINARY, name="y") 
    mclp.setObjective(gp.quicksum(a_i[i]*y[i] for i in range(I)), GRB.MAXIMIZE)
    mclp.addConstrs(gp.quicksum(x[j] for j in N_i[i]) >= y[i] for i in range (I))
    mclp.addConstr(gp.quicksum(x[j] for j in range(J)) <= P)
    mclp.optimize()
    open_stations_indices = [j for j in range(J) if x[j].x > 0.5]
    open_stations= stations.iloc[open_stations_indices]
    return open_stations, mclp.obj_val

Step 4. Evaluate the Result¶

Question 8: To evaluate the optimization result, we always compare with the current operation. Calculate current_coverage. ( 2 pts )¶

Current coverage is the sum of all the demand weights, currently covered by existing stations.
Here are the thought process you can go through.

  • Create buffers with distance S out of all the existing stations.
  • Take a unary_union of the buffers. ( 0.5 pts )
  • Use .within() function to take a subset of blocks, within the unary_union of coverage buffers. ( 0.5 pts )
  • Take the Population column out of the subset of blocks. ( 0.5 pts )
  • Take the sum of the column values. ( 0.5 pts )
In [31]:
stations['buffer'] = stations.geometry.buffer(S)
buffer_union = stations['buffer'].unary_union
covered_blocks = blocks[blocks.geometry.within(buffer_union)]
covered_population = covered_blocks['Population']
current_coverage = covered_population.sum()

Task: Check if provided code works with your defined function, solve_mclp¶

In [32]:
selecteds = []  # List to store selected stations for each value of p
obj_vals = []   # List to store objective values for each value of p

# Iterate over values of p starting from 3
for p in range(3, len(stations)+1):
    print(f"=================== for P={p}")  # Print current value of p
    # Call solve_mclp function to solve the problem for current value of p
    selected_stations, obj_val = solve_mclp(p)
    # Append selected stations to the selecteds list
    selecteds.append(selected_stations)
    # Append objective value to the obj_vals list
    obj_vals.append(obj_val)
=================== for P=3
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0xc1148ef3
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+00, 3e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 3209 columns
Presolve time: 0.00s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 28463.000000

Root relaxation: objective 1.420460e+05, 27 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    142046.00000 142046.000  0.00%     -    0s

Explored 1 nodes (27 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 142046 28463 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.420460000000e+05, best bound 1.420460000000e+05, gap 0.0000%
=================== for P=4
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0xd9224489
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [4e+00, 4e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 3209 columns
Presolve time: 0.00s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 35944.000000

Root relaxation: objective 1.535990e+05, 20 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    153599.00000 153599.000  0.00%     -    0s

Explored 1 nodes (20 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 153599 35944 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.535990000000e+05, best bound 1.535990000000e+05, gap 0.0000%
=================== for P=5
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0x1e8621a4
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [5e+00, 5e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 3209 columns
Presolve time: 0.00s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 101213.00000

Root relaxation: objective 1.578710e+05, 19 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    157871.00000 157871.000  0.00%     -    0s

Explored 1 nodes (19 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 157871 101213 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.578710000000e+05, best bound 1.578710000000e+05, gap 0.0000%
=================== for P=6
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0x4872ed6f
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [6e+00, 6e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 3209 columns
Presolve time: 0.00s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 103347.00000

Root relaxation: objective 1.615640e+05, 16 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    161564.00000 161564.000  0.00%     -    0s

Explored 1 nodes (16 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 161564 103347 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.615640000000e+05, best bound 1.615640000000e+05, gap 0.0000%
=================== for P=7
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0x50c869a2
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [7e+00, 7e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 3209 columns
Presolve time: 0.00s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 138503.00000

Root relaxation: objective 1.636980e+05, 14 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    163698.00000 163698.000  0.00%     -    0s

Explored 1 nodes (14 simplex iterations) in 0.03 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 163698 138503 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.636980000000e+05, best bound 1.636980000000e+05, gap 0.0000%
=================== for P=8
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0xc631c009
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [8e+00, 8e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 3209 columns
Presolve time: 0.00s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 139069.00000

Root relaxation: objective 1.656950e+05, 11 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    165695.00000 165695.000  0.00%     -    0s

Explored 1 nodes (11 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 165695 139069 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.656950000000e+05, best bound 1.656950000000e+05, gap 0.0000%
=================== for P=9
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0xde1bae41
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [9e+00, 9e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 3209 columns
Presolve time: 0.00s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 139439.00000

Root relaxation: objective 1.663330e+05, 11 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    166333.00000 166333.000  0.00%     -    0s

Explored 1 nodes (11 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 166333 139439 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.663330000000e+05, best bound 1.663330000000e+05, gap 0.0000%
=================== for P=10
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0xda05e924
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 3209 columns
Presolve time: 0.00s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 139558.00000

Root relaxation: objective 1.668990e+05, 6 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    166899.00000 166899.000  0.00%     -    0s

Explored 1 nodes (6 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 166899 139558 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.668990000000e+05, best bound 1.668990000000e+05, gap 0.0000%
=================== for P=11
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0x4f3e9f77
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 3209 columns
Presolve time: 0.00s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 140196.00000

Root relaxation: objective 1.671390e+05, 6 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    167139.00000 167139.000  0.00%     -    0s

Explored 1 nodes (6 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 167139 140196 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.671390000000e+05, best bound 1.671390000000e+05, gap 0.0000%
=================== for P=12
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0x1e3b83ba
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 3209 columns
Presolve time: 0.00s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 140425.00000

Root relaxation: objective 1.673330e+05, 3 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    167333.00000 167333.000  0.00%     -    0s

Explored 1 nodes (3 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 167333 140425 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.673330000000e+05, best bound 1.673330000000e+05, gap 0.0000%
=================== for P=13
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0x209b8da2
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 3209 columns
Presolve time: 0.00s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 167360.00000

Root relaxation: objective 1.674520e+05, 2 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    167452.00000 167452.000  0.00%     -    0s

Explored 1 nodes (2 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 167452 167360 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.674520000000e+05, best bound 1.674520000000e+05, gap 0.0000%
=================== for P=14
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0x03cf73b5
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 3209 columns
Presolve time: 0.00s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 167374.00000

Root relaxation: objective 1.675220e+05, 2 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    167522.00000 167522.000  0.00%     -    0s

Explored 1 nodes (2 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 167522 167374 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.675220000000e+05, best bound 1.675220000000e+05, gap 0.0000%
=================== for P=15
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0x952e5b76
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 3209 columns
Presolve time: 0.00s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 167443.00000

Root relaxation: objective 1.675910e+05, 1 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    167591.00000 167591.000  0.00%     -    0s

Explored 1 nodes (1 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 167591 167443 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.675910000000e+05, best bound 1.675910000000e+05, gap 0.0000%
=================== for P=16
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0xcd3e3dcd
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 3209 columns
Presolve time: 0.00s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 167605.00000

Explored 0 nodes (0 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 2: 167605 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676050000000e+05, best bound 1.676050000000e+05, gap 0.0000%
=================== for P=17
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0x0e5accf5
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3203 rows and 3211 columns
Presolve time: 0.00s
Presolved: 22 rows, 41 columns, 90 nonzeros
Found heuristic solution: objective 167606.00000
Variable types: 0 continuous, 41 integer (41 binary)

Explored 0 nodes (0 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
=================== for P=18
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0xbd53d068
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3210 rows and 3218 columns
Presolve time: 0.00s
Presolved: 15 rows, 34 columns, 62 nonzeros
Found heuristic solution: objective 167606.00000
Variable types: 0 continuous, 34 integer (34 binary)

Explored 0 nodes (0 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
=================== for P=19
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0x4d9615ea
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3225 rows and 3252 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 1 (of 8 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
=================== for P=20
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0x06e3d55a
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3225 rows and 3252 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 1 (of 8 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
=================== for P=21
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0xac9379a7
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3225 rows and 3252 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 1 (of 8 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
=================== for P=22
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0x294b1219
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3225 rows and 3252 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 1 (of 8 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
=================== for P=23
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0x9b75ffee
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3225 rows and 3252 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 1 (of 8 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
=================== for P=24
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0x4030e886
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3225 rows and 3252 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.00 seconds (0.00 work units)
Thread count was 1 (of 8 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
=================== for P=25
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0x80c372e9
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3225 rows and 3252 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 1 (of 8 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
=================== for P=26
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0xba252813
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+01, 3e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3225 rows and 3252 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.00 seconds (0.00 work units)
Thread count was 1 (of 8 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
=================== for P=27
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0xb06b9a49
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+01, 3e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3225 rows and 3252 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.00 seconds (0.00 work units)
Thread count was 1 (of 8 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
=================== for P=28
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0xe144439c
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+01, 3e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3225 rows and 3252 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 1 (of 8 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%

Task: Check if the output Table is plausible. And learn how to create a pandas DataFrame¶

  • To create a DataFrame, you can call pandas.DataFrame() and deliver a dictionary.
  • The dictionary will have key and value pairs.
    • key will be the column name
    • value will be an array of column values
In [33]:
results = pd.DataFrame({
    'P': range(3, len(stations)+1),
    'Coverage': obj_vals
})
results
Out[33]:
P Coverage
0 3 142046.0
1 4 153599.0
2 5 157871.0
3 6 161564.0
4 7 163698.0
5 8 165695.0
6 9 166333.0
7 10 166899.0
8 11 167139.0
9 12 167333.0
10 13 167452.0
11 14 167522.0
12 15 167591.0
13 16 167605.0
14 17 167606.0
15 18 167606.0
16 19 167606.0
17 20 167606.0
18 21 167606.0
19 22 167606.0
20 23 167606.0
21 24 167606.0
22 25 167606.0
23 26 167606.0
24 27 167606.0
25 28 167606.0
In [34]:
def scatterplot_result(results):
    # Plot the DataFrame, in scatter plot, taking P values as x and Coverage values as y
    results.plot(kind="scatter", x="P", y="Coverage")
    # Add grid lines
    plt.grid(True)
    # Add the current coverage point in color red
    plt.scatter(len(stations), current_coverage, color="red")
    # provide a dashed red line to inform current coverage
    plt.axhline(y=current_coverage, color='r', linestyle='--', label='Current Coverage')
    # show the plot!
    plt.show()
    
scatterplot_result(results)
No description has been provided for this image

Task: Put your code to plot open_stations and coverage buffer from Question 6.¶

Feel free to edit any other plotting details

In [42]:
def map_result(p, demand_block=True):
    open_stations = selecteds[p-3].copy()
    open_stations['buffer'] = open_stations.geometry.buffer(S)
    fig, ax = plt.subplots(figsize=(15, 10))
    SBC_FD.plot(ax=ax, color='none', edgecolor='blue', zorder=10)
    # blocks.plot(
    #     ax=ax,
    #     column='Population',
    #     cmap='viridis',
    #     legend=True,
    #     markersize=blocks['Population']*0.1,
    #     alpha=0.4,
    #     legend_kwds={'label':"Population"}
    # )
    open_stations.plot(ax=ax, color='green', markersize=50, label='Stations', zorder=5)
    for buffer in open_stations['buffer']:
        gpd.GeoSeries(buffer).boundary.plot(ax=ax, linestyle='--', color='black')
    if demand_block:
        blocks.plot("Population", ax=ax, legend=True, markersize=5)
    else:
        fishnet_points.plot(ax=ax)
    plt.title(f"{p} open stations and coverage buffer")
    plt.show()
    
map_result(10) # Try different p!
No description has been provided for this image

Task: Following function is to go through the whole process. Check if you get the same output as before :)¶

In [43]:
def optimize_and_evaluate(demand_block=True):
    selecteds = [] 
    obj_vals = [] 
    for p in range(3, len(stations)+1):
        print(f"=================== for P={p}")
        selected_stations, obj_val = solve_mclp(p)
        selecteds.append(selected_stations)
        obj_vals.append(obj_val)
        map_result(p, demand_block)
        
    results = pd.DataFrame({
        'P': range(3, len(stations)+1),
        'Coverage': obj_vals
    })
    scatterplot_result(results)
In [44]:
optimize_and_evaluate()
=================== for P=3
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0xc1148ef3
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+00, 3e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 3209 columns
Presolve time: 0.00s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 28463.000000

Root relaxation: objective 1.420460e+05, 27 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    142046.00000 142046.000  0.00%     -    0s

Explored 1 nodes (27 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 142046 28463 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.420460000000e+05, best bound 1.420460000000e+05, gap 0.0000%
No description has been provided for this image
=================== for P=4
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0xd9224489
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [4e+00, 4e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 3209 columns
Presolve time: 0.01s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 35944.000000

Root relaxation: objective 1.535990e+05, 20 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    153599.00000 153599.000  0.00%     -    0s

Explored 1 nodes (20 simplex iterations) in 0.03 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 153599 35944 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.535990000000e+05, best bound 1.535990000000e+05, gap 0.0000%
No description has been provided for this image
=================== for P=5
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0x1e8621a4
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [5e+00, 5e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 3209 columns
Presolve time: 0.00s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 101213.00000

Root relaxation: objective 1.578710e+05, 19 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    157871.00000 157871.000  0.00%     -    0s

Explored 1 nodes (19 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 157871 101213 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.578710000000e+05, best bound 1.578710000000e+05, gap 0.0000%
No description has been provided for this image
=================== for P=6
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0x4872ed6f
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [6e+00, 6e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 3209 columns
Presolve time: 0.00s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 103347.00000

Root relaxation: objective 1.615640e+05, 16 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    161564.00000 161564.000  0.00%     -    0s

Explored 1 nodes (16 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 161564 103347 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.615640000000e+05, best bound 1.615640000000e+05, gap 0.0000%
No description has been provided for this image
=================== for P=7
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0x50c869a2
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [7e+00, 7e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 3209 columns
Presolve time: 0.00s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 138503.00000

Root relaxation: objective 1.636980e+05, 14 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    163698.00000 163698.000  0.00%     -    0s

Explored 1 nodes (14 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 163698 138503 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.636980000000e+05, best bound 1.636980000000e+05, gap 0.0000%
No description has been provided for this image
=================== for P=8
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0xc631c009
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [8e+00, 8e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 3209 columns
Presolve time: 0.00s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 139069.00000

Root relaxation: objective 1.656950e+05, 11 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    165695.00000 165695.000  0.00%     -    0s

Explored 1 nodes (11 simplex iterations) in 0.03 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 165695 139069 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.656950000000e+05, best bound 1.656950000000e+05, gap 0.0000%
No description has been provided for this image
=================== for P=9
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0xde1bae41
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [9e+00, 9e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 3209 columns
Presolve time: 0.00s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 139439.00000

Root relaxation: objective 1.663330e+05, 11 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    166333.00000 166333.000  0.00%     -    0s

Explored 1 nodes (11 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 166333 139439 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.663330000000e+05, best bound 1.663330000000e+05, gap 0.0000%
No description has been provided for this image
=================== for P=10
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0xda05e924
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 3209 columns
Presolve time: 0.00s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 139558.00000

Root relaxation: objective 1.668990e+05, 6 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    166899.00000 166899.000  0.00%     -    0s

Explored 1 nodes (6 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 166899 139558 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.668990000000e+05, best bound 1.668990000000e+05, gap 0.0000%
No description has been provided for this image
=================== for P=11
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0x4f3e9f77
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 3209 columns
Presolve time: 0.00s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 140196.00000

Root relaxation: objective 1.671390e+05, 6 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    167139.00000 167139.000  0.00%     -    0s

Explored 1 nodes (6 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 167139 140196 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.671390000000e+05, best bound 1.671390000000e+05, gap 0.0000%
No description has been provided for this image
=================== for P=12
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0x1e3b83ba
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 3209 columns
Presolve time: 0.00s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 140425.00000

Root relaxation: objective 1.673330e+05, 3 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    167333.00000 167333.000  0.00%     -    0s

Explored 1 nodes (3 simplex iterations) in 0.03 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 167333 140425 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.673330000000e+05, best bound 1.673330000000e+05, gap 0.0000%
No description has been provided for this image
=================== for P=13
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0x209b8da2
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 3209 columns
Presolve time: 0.00s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 167360.00000

Root relaxation: objective 1.674520e+05, 2 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    167452.00000 167452.000  0.00%     -    0s

Explored 1 nodes (2 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 167452 167360 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.674520000000e+05, best bound 1.674520000000e+05, gap 0.0000%
No description has been provided for this image
=================== for P=14
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0x03cf73b5
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 3209 columns
Presolve time: 0.00s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 167374.00000

Root relaxation: objective 1.675220e+05, 2 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    167522.00000 167522.000  0.00%     -    0s

Explored 1 nodes (2 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 167522 167374 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.675220000000e+05, best bound 1.675220000000e+05, gap 0.0000%
No description has been provided for this image
=================== for P=15
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0x952e5b76
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 3209 columns
Presolve time: 0.00s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 167443.00000

Root relaxation: objective 1.675910e+05, 1 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    167591.00000 167591.000  0.00%     -    0s

Explored 1 nodes (1 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 167591 167443 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.675910000000e+05, best bound 1.675910000000e+05, gap 0.0000%
No description has been provided for this image
=================== for P=16
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0xcd3e3dcd
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 3209 columns
Presolve time: 0.00s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 167605.00000

Explored 0 nodes (0 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 2: 167605 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676050000000e+05, best bound 1.676050000000e+05, gap 0.0000%
No description has been provided for this image
=================== for P=17
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0x0e5accf5
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3203 rows and 3211 columns
Presolve time: 0.00s
Presolved: 22 rows, 41 columns, 90 nonzeros
Found heuristic solution: objective 167606.00000
Variable types: 0 continuous, 41 integer (41 binary)

Explored 0 nodes (0 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
No description has been provided for this image
=================== for P=18
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0xbd53d068
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3210 rows and 3218 columns
Presolve time: 0.00s
Presolved: 15 rows, 34 columns, 62 nonzeros
Found heuristic solution: objective 167606.00000
Variable types: 0 continuous, 34 integer (34 binary)

Explored 0 nodes (0 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
No description has been provided for this image
=================== for P=19
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0x4d9615ea
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3225 rows and 3252 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.00 seconds (0.00 work units)
Thread count was 1 (of 8 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
No description has been provided for this image
=================== for P=20
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0x06e3d55a
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3225 rows and 3252 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.03 seconds (0.00 work units)
Thread count was 1 (of 8 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
No description has been provided for this image
=================== for P=21
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0xac9379a7
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3225 rows and 3252 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.00 seconds (0.00 work units)
Thread count was 1 (of 8 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
No description has been provided for this image
=================== for P=22
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0x294b1219
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3225 rows and 3252 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.00 seconds (0.00 work units)
Thread count was 1 (of 8 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
No description has been provided for this image
=================== for P=23
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0x9b75ffee
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3225 rows and 3252 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 1 (of 8 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
No description has been provided for this image
=================== for P=24
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0x4030e886
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3225 rows and 3252 columns
Presolve time: 0.01s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 1 (of 8 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
No description has been provided for this image
=================== for P=25
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0x80c372e9
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3225 rows and 3252 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 1 (of 8 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
No description has been provided for this image
=================== for P=26
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0xba252813
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+01, 3e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3225 rows and 3252 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.02 seconds (0.00 work units)
Thread count was 1 (of 8 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
No description has been provided for this image
=================== for P=27
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0xb06b9a49
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+01, 3e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3225 rows and 3252 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 1 (of 8 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
No description has been provided for this image
=================== for P=28
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0xe144439c
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+01, 3e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3225 rows and 3252 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.00 seconds (0.00 work units)
Thread count was 1 (of 8 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
No description has been provided for this image
No description has been provided for this image

Step 4. Replicate your Analysis with different Demand Representations¶

Task: Review from Lab 2. We are creating fishnet points within the SBC_FD¶

In [45]:
boundary = SBC_FD.envelope # .envelope gives you the bounding rectangle of given GeoDataFrame.
boundary.bounds
Out[45]:
minx miny maxx maxy
0 -61331.613 -401270.1778 50847.5684 -323367.7559
In [46]:
minx, miny, maxx, maxy = boundary.loc[0].bounds
print(minx, miny, maxx, maxy)
-61331.61300000176 -401270.1777999997 50847.56839999929 -323367.7559000002
In [47]:
from shapely.geometry import Point

# Here, we are going to create fishnet points.
    # Fishnet points are points spaced with an equal interval.
    # You'll see when you see the output!

# Define the interval between points 
#### Note: Adjust interval value as needed for lab question 2
def create_fishnet(interval):
# Create arrays of x and y coordinates using np.arange
    x_coords = np.arange(minx, maxx, interval)
    y_coords = np.arange(miny, maxy, interval)

    # Create a list to store the points
    fishnet_points = []

    # Generate points for the fishnet
    for y in y_coords:
        for x in x_coords:
            fishnet_points.append((x, y))

    # Print the number of points generated
    print("Number of points in the fishnet:", len(fishnet_points))

    fishnet_points = gpd.GeoSeries([Point(pt_cd) for pt_cd in fishnet_points])
    fishnet_points = fishnet_points[fishnet_points.within(SBC_FD.geometry[0])]
    fishnet_points.plot(figsize=(15,5))
    return fishnet_points
In [55]:
interval = 5280/5  # default: 5280/5 feet (1 mile / 5 = 0.2 mile) 
fishnet_points = create_fishnet(interval)
Number of points in the fishnet: 7918
No description has been provided for this image
In [56]:
# Current Coverage
current_coverage = fishnet_points.within(stations.buffer(S).unary_union).sum()
current_coverage
Out[56]:
1795

Question 9: Re-compute the model variables here for fishnet_points, instead of blocks. ( 1 pt )¶

Note: all the fishnet points will have the same weight, 1.

In [57]:
fishnet_points =  fishnet_points.reset_index(drop=True)
I = len(fishnet_points)
J = len(stations)
a_i = [1 for i in range(I)]
D_ij = [[np.sqrt((fishnet_points.x[i] - stations.geometry.x[j])**2 + (fishnet_points.y[i] - stations.geometry.y[j])**2)
         for j in range(J)] for i in range(I)]
N_i = dict(zip(range(I), [[] for _ in range(I)]))
for i in range(I):
    for j in range(J):
        if D_ij[i][j] <= S:
            N_i[i].append(j)
In [58]:
optimize_and_evaluate(demand_block=False)
=================== for P=3
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0x3f7c710c
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+00, 3e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 3263 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 506.0000000

Root relaxation: objective 5.400000e+02, 45 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0     540.0000000  540.00000  0.00%     -    0s

Explored 1 nodes (45 simplex iterations) in 0.02 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 540 506 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 5.400000000000e+02, best bound 5.400000000000e+02, gap 0.0000%
No description has been provided for this image
=================== for P=4
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0xa01cdfc9
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [4e+00, 4e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 3263 columns
Presolve time: 0.00s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 582.0000000

Root relaxation: objective 7.040000e+02, 46 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0     704.0000000  704.00000  0.00%     -    0s

Explored 1 nodes (46 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 704 582 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 7.040000000000e+02, best bound 7.040000000000e+02, gap 0.0000%
No description has been provided for this image
=================== for P=5
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0xb95f9119
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [5e+00, 5e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 3263 columns
Presolve time: 0.00s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 675.0000000

Root relaxation: objective 8.550000e+02, 43 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0     855.0000000  855.00000  0.00%     -    0s

Explored 1 nodes (43 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 855 675 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 8.550000000000e+02, best bound 8.550000000000e+02, gap 0.0000%
No description has been provided for this image
=================== for P=6
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0xdc018ef8
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [6e+00, 6e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 3263 columns
Presolve time: 0.00s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 746.0000000

Root relaxation: objective 1.005000e+03, 39 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1005.0000000 1005.00000  0.00%     -    0s

Explored 1 nodes (39 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 1005 746 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.005000000000e+03, best bound 1.005000000000e+03, gap 0.0000%
No description has been provided for this image
=================== for P=7
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0xd4eb132b
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [7e+00, 7e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 3263 columns
Presolve time: 0.00s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 929.0000000

Root relaxation: objective 1.146000e+03, 38 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1146.0000000 1146.00000  0.00%     -    0s

Explored 1 nodes (38 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 1146 929 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.146000000000e+03, best bound 1.146000000000e+03, gap 0.0000%
No description has been provided for this image
=================== for P=8
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0x05e3c257
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [8e+00, 8e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 3263 columns
Presolve time: 0.00s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1086.0000000

Root relaxation: objective 1.270000e+03, 30 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1270.0000000 1270.00000  0.00%     -    0s

Explored 1 nodes (30 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 1270 1086 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.270000000000e+03, best bound 1.270000000000e+03, gap 0.0000%
No description has been provided for this image
=================== for P=9
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0xf7ea4d1e
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [9e+00, 9e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 3263 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1177.0000000

Root relaxation: objective 1.384000e+03, 30 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1384.0000000 1384.00000  0.00%     -    0s

Explored 1 nodes (30 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 1384 1177 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.384000000000e+03, best bound 1.384000000000e+03, gap 0.0000%
No description has been provided for this image
=================== for P=10
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0x7467d208
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 3263 columns
Presolve time: 0.00s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1291.0000000

Root relaxation: objective 1.475000e+03, 27 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1475.0000000 1475.00000  0.00%     -    0s

Explored 1 nodes (27 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 1475 1291 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.475000000000e+03, best bound 1.475000000000e+03, gap 0.0000%
No description has been provided for this image
=================== for P=11
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0x10c3d27f
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 3263 columns
Presolve time: 0.00s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1433.0000000

Root relaxation: objective 1.564000e+03, 27 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1564.0000000 1564.00000  0.00%     -    0s

Explored 1 nodes (27 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 1564 1433 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.564000000000e+03, best bound 1.564000000000e+03, gap 0.0000%
No description has been provided for this image
=================== for P=12
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0x649633df
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 3263 columns
Presolve time: 0.00s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1493.0000000

Root relaxation: objective 1.647000e+03, 27 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1647.0000000 1647.00000  0.00%     -    0s

Explored 1 nodes (27 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 1647 1493 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.647000000000e+03, best bound 1.647000000000e+03, gap 0.0000%
No description has been provided for this image
=================== for P=13
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0x9b95d984
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 3263 columns
Presolve time: 0.00s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1591.0000000

Root relaxation: objective 1.715000e+03, 18 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1715.0000000 1715.00000  0.00%     -    0s

Explored 1 nodes (18 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 1715 1591 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.715000000000e+03, best bound 1.715000000000e+03, gap 0.0000%
No description has been provided for this image
=================== for P=14
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0xdadf5112
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 3263 columns
Presolve time: 0.00s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1611.0000000

Root relaxation: objective 1.743000e+03, 17 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1743.0000000 1743.00000  0.00%     -    0s

Explored 1 nodes (17 simplex iterations) in 0.03 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 1743 1611 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.743000000000e+03, best bound 1.743000000000e+03, gap 0.0000%
No description has been provided for this image
=================== for P=15
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0xe090a64f
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 3263 columns
Presolve time: 0.00s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1646.0000000

Root relaxation: objective 1.763000e+03, 14 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1763.0000000 1763.00000  0.00%     -    0s

Explored 1 nodes (14 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 1763 1646 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.763000000000e+03, best bound 1.763000000000e+03, gap 0.0000%
No description has been provided for this image
=================== for P=16
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0xc848a4a7
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 3263 columns
Presolve time: 0.00s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1714.0000000

Root relaxation: objective 1.780000e+03, 8 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1780.0000000 1780.00000  0.00%     -    0s

Explored 1 nodes (8 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 1780 1714 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.780000000000e+03, best bound 1.780000000000e+03, gap 0.0000%
No description has been provided for this image
=================== for P=17
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0x743280a7
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 3263 columns
Presolve time: 0.00s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1789.0000000

Root relaxation: cutoff, 3 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

     0     0     cutoff    0      1789.00000 1789.00000  0.00%     -    0s

Explored 1 nodes (3 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 2: 1789 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.789000000000e+03, best bound 1.789000000000e+03, gap 0.0000%
No description has been provided for this image
=================== for P=18
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0xbb43ee56
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 3263 columns
Presolve time: 0.00s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1793.0000000

Root relaxation: infeasible, 1 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

     0     0 infeasible    0      1793.00000 1793.00000  0.00%     -    0s

Explored 1 nodes (1 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 2: 1793 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.793000000000e+03, best bound 1.793000000000e+03, gap 0.0000%
No description has been provided for this image
=================== for P=19
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0xa9cc7751
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 3263 columns
Presolve time: 0.00s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1797.0000000

Explored 0 nodes (0 simplex iterations) in 0.03 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 2: 1797 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
No description has been provided for this image
=================== for P=20
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0x3c5cc094
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3261 rows and 3264 columns
Presolve time: 0.00s
Presolved: 44 rows, 68 columns, 192 nonzeros
Found heuristic solution: objective 1797.0000000
Variable types: 0 continuous, 68 integer (68 binary)

Explored 0 nodes (0 simplex iterations) in 0.00 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 2: 1797 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
No description has been provided for this image
=================== for P=21
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0xa72ab122
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3264 rows and 3267 columns
Presolve time: 0.00s
Presolved: 41 rows, 65 columns, 174 nonzeros
Found heuristic solution: objective 1797.0000000
Variable types: 0 continuous, 65 integer (65 binary)

Explored 0 nodes (0 simplex iterations) in 0.00 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 2: 1797 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
No description has been provided for this image
=================== for P=22
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0xf698ea55
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3272 rows and 3275 columns
Presolve time: 0.00s
Presolved: 33 rows, 57 columns, 134 nonzeros
Found heuristic solution: objective 1797.0000000
Variable types: 0 continuous, 57 integer (57 binary)

Explored 0 nodes (0 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 2: 1797 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
No description has been provided for this image
=================== for P=23
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0xf679243a
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3285 rows and 3288 columns
Presolve time: 0.00s
Presolved: 20 rows, 44 columns, 82 nonzeros
Found heuristic solution: objective 1797.0000000
Variable types: 0 continuous, 44 integer (44 binary)

Explored 0 nodes (0 simplex iterations) in 0.00 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 2: 1797 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
No description has been provided for this image
=================== for P=24
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0x63944ca0
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3305 rows and 3332 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.00 seconds (0.00 work units)
Thread count was 1 (of 8 available processors)

Solution count 2: 1797 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
No description has been provided for this image
=================== for P=25
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0x32ab1ba6
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3305 rows and 3332 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.00 seconds (0.00 work units)
Thread count was 1 (of 8 available processors)

Solution count 2: 1797 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
No description has been provided for this image
=================== for P=26
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0xaedb8953
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+01, 3e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3305 rows and 3332 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.00 seconds (0.00 work units)
Thread count was 1 (of 8 available processors)

Solution count 2: 1797 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
No description has been provided for this image
=================== for P=27
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0xa6b75529
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+01, 3e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3305 rows and 3332 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.00 seconds (0.00 work units)
Thread count was 1 (of 8 available processors)

Solution count 2: 1797 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
No description has been provided for this image
=================== for P=28
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0xe7946d32
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+01, 3e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3305 rows and 3332 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.00 seconds (0.00 work units)
Thread count was 1 (of 8 available processors)

Solution count 2: 1797 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
No description has been provided for this image
No description has been provided for this image

Task: Repeat the whole process with another fishnet_points with different fishnet interval.¶

In [59]:
interval = 10560/5  # default: 5280/5 feet (1 mile / 5 = 0.2 mile) 
fishnet_points = create_fishnet(interval)
Number of points in the fishnet: 1998
No description has been provided for this image
In [60]:
optimize_and_evaluate(demand_block=False)
=================== for P=3
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0x3f7c710c
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+00, 3e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 3263 columns
Presolve time: 0.03s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 506.0000000

Root relaxation: objective 5.400000e+02, 45 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0     540.0000000  540.00000  0.00%     -    0s

Explored 1 nodes (45 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 540 506 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 5.400000000000e+02, best bound 5.400000000000e+02, gap 0.0000%
No description has been provided for this image
=================== for P=4
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0xa01cdfc9
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [4e+00, 4e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 3263 columns
Presolve time: 0.00s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 582.0000000

Root relaxation: objective 7.040000e+02, 46 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0     704.0000000  704.00000  0.00%     -    0s

Explored 1 nodes (46 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 704 582 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 7.040000000000e+02, best bound 7.040000000000e+02, gap 0.0000%
No description has been provided for this image
=================== for P=5
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0xb95f9119
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [5e+00, 5e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 3263 columns
Presolve time: 0.00s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 675.0000000

Root relaxation: objective 8.550000e+02, 43 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0     855.0000000  855.00000  0.00%     -    0s

Explored 1 nodes (43 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 855 675 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 8.550000000000e+02, best bound 8.550000000000e+02, gap 0.0000%
No description has been provided for this image
=================== for P=6
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0xdc018ef8
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [6e+00, 6e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 3263 columns
Presolve time: 0.00s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 746.0000000

Root relaxation: objective 1.005000e+03, 39 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1005.0000000 1005.00000  0.00%     -    0s

Explored 1 nodes (39 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 1005 746 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.005000000000e+03, best bound 1.005000000000e+03, gap 0.0000%
No description has been provided for this image
=================== for P=7
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0xd4eb132b
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [7e+00, 7e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 3263 columns
Presolve time: 0.00s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 929.0000000

Root relaxation: objective 1.146000e+03, 38 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1146.0000000 1146.00000  0.00%     -    0s

Explored 1 nodes (38 simplex iterations) in 0.02 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 1146 929 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.146000000000e+03, best bound 1.146000000000e+03, gap 0.0000%
No description has been provided for this image
=================== for P=8
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0x05e3c257
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [8e+00, 8e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 3263 columns
Presolve time: 0.00s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1086.0000000

Root relaxation: objective 1.270000e+03, 30 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1270.0000000 1270.00000  0.00%     -    0s

Explored 1 nodes (30 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 1270 1086 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.270000000000e+03, best bound 1.270000000000e+03, gap 0.0000%
No description has been provided for this image
=================== for P=9
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0xf7ea4d1e
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [9e+00, 9e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 3263 columns
Presolve time: 0.00s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1177.0000000

Root relaxation: objective 1.384000e+03, 30 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1384.0000000 1384.00000  0.00%     -    0s

Explored 1 nodes (30 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 1384 1177 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.384000000000e+03, best bound 1.384000000000e+03, gap 0.0000%
No description has been provided for this image
=================== for P=10
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0x7467d208
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 3263 columns
Presolve time: 0.00s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1291.0000000

Root relaxation: objective 1.475000e+03, 27 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1475.0000000 1475.00000  0.00%     -    0s

Explored 1 nodes (27 simplex iterations) in 0.03 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 1475 1291 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.475000000000e+03, best bound 1.475000000000e+03, gap 0.0000%
No description has been provided for this image
=================== for P=11
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0x10c3d27f
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 3263 columns
Presolve time: 0.00s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1433.0000000

Root relaxation: objective 1.564000e+03, 27 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1564.0000000 1564.00000  0.00%     -    0s

Explored 1 nodes (27 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 1564 1433 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.564000000000e+03, best bound 1.564000000000e+03, gap 0.0000%
No description has been provided for this image
=================== for P=12
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0x649633df
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 3263 columns
Presolve time: 0.00s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1493.0000000

Root relaxation: objective 1.647000e+03, 27 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1647.0000000 1647.00000  0.00%     -    0s

Explored 1 nodes (27 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 1647 1493 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.647000000000e+03, best bound 1.647000000000e+03, gap 0.0000%
No description has been provided for this image
=================== for P=13
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0x9b95d984
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 3263 columns
Presolve time: 0.00s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1591.0000000

Root relaxation: objective 1.715000e+03, 18 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1715.0000000 1715.00000  0.00%     -    0s

Explored 1 nodes (18 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 1715 1591 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.715000000000e+03, best bound 1.715000000000e+03, gap 0.0000%
No description has been provided for this image
=================== for P=14
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0xdadf5112
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 3263 columns
Presolve time: 0.00s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1611.0000000

Root relaxation: objective 1.743000e+03, 17 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1743.0000000 1743.00000  0.00%     -    0s

Explored 1 nodes (17 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 1743 1611 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.743000000000e+03, best bound 1.743000000000e+03, gap 0.0000%
No description has been provided for this image
=================== for P=15
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0xe090a64f
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 3263 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1646.0000000

Root relaxation: objective 1.763000e+03, 14 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1763.0000000 1763.00000  0.00%     -    0s

Explored 1 nodes (14 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 1763 1646 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.763000000000e+03, best bound 1.763000000000e+03, gap 0.0000%
No description has been provided for this image
=================== for P=16
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0xc848a4a7
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 3263 columns
Presolve time: 0.00s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1714.0000000

Root relaxation: objective 1.780000e+03, 8 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1780.0000000 1780.00000  0.00%     -    0s

Explored 1 nodes (8 simplex iterations) in 0.04 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 1780 1714 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.780000000000e+03, best bound 1.780000000000e+03, gap 0.0000%
No description has been provided for this image
=================== for P=17
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0x743280a7
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 3263 columns
Presolve time: 0.00s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1789.0000000

Root relaxation: cutoff, 3 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

     0     0     cutoff    0      1789.00000 1789.00000  0.00%     -    0s

Explored 1 nodes (3 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 2: 1789 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.789000000000e+03, best bound 1.789000000000e+03, gap 0.0000%
No description has been provided for this image
=================== for P=18
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0xbb43ee56
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 3263 columns
Presolve time: 0.00s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1793.0000000

Root relaxation: infeasible, 1 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

     0     0 infeasible    0      1793.00000 1793.00000  0.00%     -    0s

Explored 1 nodes (1 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 2: 1793 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.793000000000e+03, best bound 1.793000000000e+03, gap 0.0000%
No description has been provided for this image
=================== for P=19
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0xa9cc7751
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 3263 columns
Presolve time: 0.00s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1797.0000000

Explored 0 nodes (0 simplex iterations) in 0.00 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 2: 1797 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
No description has been provided for this image
=================== for P=20
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0x3c5cc094
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3261 rows and 3264 columns
Presolve time: 0.00s
Presolved: 44 rows, 68 columns, 192 nonzeros
Found heuristic solution: objective 1797.0000000
Variable types: 0 continuous, 68 integer (68 binary)

Explored 0 nodes (0 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 2: 1797 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
No description has been provided for this image
=================== for P=21
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0xa72ab122
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3264 rows and 3267 columns
Presolve time: 0.00s
Presolved: 41 rows, 65 columns, 174 nonzeros
Found heuristic solution: objective 1797.0000000
Variable types: 0 continuous, 65 integer (65 binary)

Explored 0 nodes (0 simplex iterations) in 0.03 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 2: 1797 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
No description has been provided for this image
=================== for P=22
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0xf698ea55
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3272 rows and 3275 columns
Presolve time: 0.00s
Presolved: 33 rows, 57 columns, 134 nonzeros
Found heuristic solution: objective 1797.0000000
Variable types: 0 continuous, 57 integer (57 binary)

Explored 0 nodes (0 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 2: 1797 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
No description has been provided for this image
=================== for P=23
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0xf679243a
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3285 rows and 3288 columns
Presolve time: 0.00s
Presolved: 20 rows, 44 columns, 82 nonzeros
Found heuristic solution: objective 1797.0000000
Variable types: 0 continuous, 44 integer (44 binary)

Explored 0 nodes (0 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 2: 1797 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
No description has been provided for this image
=================== for P=24
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0x63944ca0
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3305 rows and 3332 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.00 seconds (0.00 work units)
Thread count was 1 (of 8 available processors)

Solution count 2: 1797 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
No description has been provided for this image
=================== for P=25
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0x32ab1ba6
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3305 rows and 3332 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 1 (of 8 available processors)

Solution count 2: 1797 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
No description has been provided for this image
=================== for P=26
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0xaedb8953
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+01, 3e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3305 rows and 3332 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 1 (of 8 available processors)

Solution count 2: 1797 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
No description has been provided for this image
=================== for P=27
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0xa6b75529
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+01, 3e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3305 rows and 3332 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.00 seconds (0.00 work units)
Thread count was 1 (of 8 available processors)

Solution count 2: 1797 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
No description has been provided for this image
=================== for P=28
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 21.2.0 21C52)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0xe7946d32
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+01, 3e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3305 rows and 3332 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.00 seconds (0.00 work units)
Thread count was 1 (of 8 available processors)

Solution count 2: 1797 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
No description has been provided for this image
No description has been provided for this image

Question 10: Compare the Scatter plots out of Blocks, 0.2 mile fishnet points, and another fishnet points with interval of your choice. Discuss the insights you can get. ( 5 pts )¶

In Lab 2, we discovered that different Coverage Distance Standard can impact the coverage analysis result.
In Lab 4, we can discover how different demand representation makes difference.
Share your insights about

  • provide three scatter plots ( 3 pts )
  • how SBC_FD is currently doing with existing stations in terms of coverage ( 1 pt )
  • how demand representation impacts the coverage analysis ( 1 pt )

TIP: you can copy and paste your screenshot into markdown cells

  • Here are three scatter plots:
    1. scatter plots out of blocks

image.png

2. 0.2 mile fishnet points

image.png

3. 0.4 mile fishnet points

image.png

  • Through observing the plots, the coverage circles indicate that some areas are well covered, but there are some gaps in coverage where no station covers certain blocks or fishnet points. This highlights areas that may need additional stations to ensure better coverage. Specifically, it suggests that even while the stations are now positioned effectively in many places, there are still some areas that need to gain from improved positioning or more stations.

  • Comparing between 0.2 mile and 0.4 mile fishnet points, we find that 0.2 mile fishnet points provide a denser demand representation than 0.4 mile fishnet points, showing more detailed coverage distances. In this regard, I think a lower interval like 0.2 mile in demand representation can help us make more precise decisions in optimizing the number and placement of stations needed.

In [ ]: